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Solution for systems of difference equations of rational form of order two

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Abstract

In this paper, we deal with the existence of solutions and the periodicity character of the following systems of rational difference equations with order two

$$\begin{aligned} x_{n+1}=\frac{x_{n}y_{n-1}}{y_{n}\left( \pm 1+x_{n}y_{n-1}\right) },\ \ \;y_{n+1}=\frac{y_{n}x_{n-1}}{x_{n}\left( \pm 1\pm y_{n}x_{n-1}\right) }, \end{aligned}$$

with initial conditions \(x_{-1},\ x_{0},\ y_{-1}\ {and}\ y_{0}\) are nonzero real numbers.

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Authors and Affiliations

  1. Mathematics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia

    E. M. Elsayed

  2. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    E. M. Elsayed

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  1. E. M. Elsayed
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Correspondence to E. M. Elsayed.

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Communicated by Jinyun Yuan.

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Elsayed, E.M. Solution for systems of difference equations of rational form of order two. Comp. Appl. Math. 33, 751–765 (2014). https://doi.org/10.1007/s40314-013-0092-9

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  • DOI: https://doi.org/10.1007/s40314-013-0092-9

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